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Abstract:

An ophthalmic lens for modifying or reducing non-axisymmetric higher
order aberrations includes an optic body disposed about an optical axis
having a primary meridian and an orthogonal secondary meridian. The optic
body comprises an anterior surface and an opposing posterior surface. The
optic body includes an optic zone comprising a base shape that is
configured to form an image or focus from light incident on the surfaces,
either alone or when used within an optical system. The optic body also
includes a higher order toric shape that is imposed on or added to one of
the surfaces. The higher order toric shape also includes a first profile
disposed along the primary meridian and a second profile disposed along
the secondary meridian that is different in shape from the first profile.
The higher order toric shape is characterized by a profile along at least
one meridian of the lens that changes with increasing radius from the
optical axis raised to a power that is greater than two.

Claims:

1. An ophthalmic lens, comprising: an optic body disposed about an
optical axis having a primary meridian and an orthogonal secondary
meridian, the optic body comprising an anterior surface and an opposing
posterior surface, the optic body including an optic zone comprising a
base shape configured to form an image from light incident on the
surfaces; a higher order tonic shape imposed on one of the surfaces, the
higher order toric shape including a first profile disposed along the
primary meridian and a second profile disposed along the secondary
meridian that is different in shape from the first profile, the higher
order tonic shape being characterized by a profile along at least one
meridian of the ophthalmic lens that changes with increasing radius from
the optical axis raised to a power that is greater than two.

2. The ophthalmic lens of claim 1, wherein one or more of the first
profile and the second profile is characterized by a profile that changes
with increasing radius from the optical axis raised to a power that is
greater than two.

3. The ophthalmic lens of claim 1, wherein the profile of the higher
order toric shape along at least one meridian of the optic body is
characterized by a polynomial equation including a term that changes
according to radius from the optical axis raised to a power that is
greater than two.

4. The ophthalmic lens of claim 1, wherein at least one of the anterior
surface and the posterior surface includes an axisymmetric aspheric shape
characterized by a conoid of rotation defined by a profile defined by a
base curvature and a conic constant.

5. The ophthalmic lens of claim 4, wherein one of or both the higher
order toric shape are located on one surface of the optic body and the
axisymmetric aspheric shape is located an opposite surface of the optic
body.

6. The ophthalmic lens of claim 1, further comprising a base toric shape
imposed on one of the surfaces, the base tone shape including a low power
meridian having a low optical power and a high power meridian having a
high optical power equal to the low optical power plus a cylinder optical
power.

7. The ophthalmic lens of claim 6, wherein the primary meridian is
coplanar in a plane parallel to the optical axis with one of the low
power meridian and the high power meridian.

8. The ophthalmic lens of claim 6, wherein the base tonic shape and the
higher order tonic shape are disposed on a same surface of the optic
body.

9. The ophthalmic lens of claim 6, wherein the base toric shape is
characterized by the equation:
z=A20x2+A11xy+A02y2 where x and y are
independent coordinate values along an x-axis and a y-axis, respectively,
z is a surface coordinate value along a z-axis that is perpendicular to
the x and y axes, and A20, A11, and A02 are polynomial
coefficients of the equation, at least two of the polynomial coefficients
being non-zero.

10. The ophthalmic lens of claim 6, wherein a sag z of the anterior
surface or the posterior surface is characterized by the equation: z
= cr 2 1 + 1 - ( 1 + k ) c 2 r 2 + A 20 x
2 + A 02 y 2 + A 40 x 4 + A 04 y 4 + A 22
x 2 y 2 + A 60 x 6 + A 06 y 6 + A 42 x 4
y 2 + A 24 x 2 y 4 ##EQU00007## where x and y are
independent coordinate values along an x-axis and a y-axis, respectively,
z is a surface sag coordinate value along a z-axis perpendicular to the x
and y axes, r2 is equal to x2+y2, c is a base curvature, k
is a conic constant, and A20, A02 are polynomial coefficients
characterizing the base tonic shape, and A40, A04, A22,
A60, A06, A42, and A24 are polynomial coefficients
characterizing the higher order toric shape, wherein one or more of the
following is true: one or more of A22, A42, and A24 is
non-zero; one or more of A40 and A04 is non-zero, wherein
A40 does not equal A04; one or more of A60 and A06 is
non-zero, wherein A60 does not equal A06; and the equation
includes at least one non-zero polynomial term that includes at least one
of x raised to an odd power and y raised to an odd power.

12. The ophthalmic lens of claim 10, wherein a sag z of the anterior
surface or the posterior surface is characterized by the equation:

13. The ophthalmic lens of claim 10, wherein the values of one or more of
k, A20, A02, A40, A04, A22, A60, A06,
A42, and A24 are determined based on a corneal shape, the
corneal shape being selected from the group consisting of the shape of a
cornea of a particular eye and an average corneal shape of a population
of eyes.

14. The ophthalmic lens of claim 6, wherein the higher order tonic shape
is characterized by the equation:
z=A40x4+A04y4+A22x2y2+A60x6+-
A06+y6+A32x2y2+A24x2y4 where x
and y are independent coordinate values along an x-axis and a y-axis,
respectively, z is a surface coordinate value along a z-axis that is
perpendicular to the x and y axes, and A40, A04, A22,
A60, A06, A42, and A24 are polynomial coefficients of
the equation.

15. The ophthalmic lens of claim 6, wherein a sag z of the anterior
surface or the posterior surface is characterized by the equation: z
= cr 2 1 + 1 - ( 1 + k ) c 2 r 2 + A 40 x
4 + A 04 y 4 + A 22 x 2 y 2 + A 60 x 6 +
A 06 y 6 + A 42 x 4 y 2 + A 24 x 2 y 4
##EQU00009## where x and y are independent coordinate values along
an x-axis and a y-axis, respectively, z is a surface sag coordinate value
along a z-axis perpendicular to the x and y axes, r2 is equal to
x2+y2, c is a base curvature, k is a conic constant, and
A20, A11, A02 are polynomial coefficients characterizing
the base tonic shape, and A40, A04, A22, A60,
A06, A42, and A24 are polynomial coefficients
characterizing the higher order toric shape, wherein one or more of the
following is true: one or more of A22, A42, and A24 is
non-zero; one or more of A40 and A04 is non-zero, wherein
A40 does not equal A04; one or more of A60 and A06 is
non-zero, wherein A60 does not equal A06; and the equation
includes at least one non-zero polynomial term that includes at least one
of x raised to an odd power and y raised to an odd power.

16. The ophthalmic lens of claim 1, wherein a sag z of the anterior
surface or the posterior surface is characterized by the equation: z =
c 1 x 2 + c 2 y 2 1 + 1 - ( 1 + k 1 ) c 1
2 x 2 + ( 1 + k 2 ) c 2 2 x 2 + A 40 x 4
+ A 04 y 4 + A 22 x 2 y 2 + A 60 x 6 + A
06 y 6 + A 42 x 4 y 2 + A 24 x 2 y 4
##EQU00010## where x and y are independent coordinate values along an
x-axis and a y-axis, respectively, z is a surface sag coordinate value
along a z-axis perpendicular to the x and y axes, r2 is equal to
x2+y2, where c1 is the base curvature along a first
meridian of the optic body, k1 is the conic constant along the first
meridian, c2 is the base curvature along a second meridian of the
optic body, k2 is the conic constant along the second meridian, and
A40, A04, A22, A60, A06, A42, and A24
are polynomial coefficients characterizing the higher order tonic shape,
wherein one or more of the following is true: one or more of A22,
A42, and A24 is non-zero; one or more of A40 and A04
is non-zero, wherein A40 does not equal A04; one or more of
A60 and A06 is non-zero, wherein A60 does not equal
A06; and the equation includes at least one non-zero polynomial term
that includes at least one of x raised to an odd power and y raised to an
odd power.

17. The ophthalmic lens of claim 1, wherein the ophthalmic lens is an
intraocular lens including one or more haptics extending from the optic
body

18. The ophthalmic lens of claim 1, wherein the ophthalmic lens is
selected from the group consisting of an intraocular lens, a contact lens
and, a corneal implant.

19. A method of producing an ophthalmic element, comprising: providing a
model cornea, the model cornea characterized by one or more of: an
aspheric profile along a first meridian of the model cornea that is
different from an aspheric profile along an orthogonal second meridian of
the model cornea; one or more of fifth-order, seventh-order, and
ninth-order aberrations; and an asphericity of a first zone of the model
cornea that is different from an asphericity of a second zone of the
model cornea surrounding the first zone; providing a model ophthalmic
element disposed about an optical axis having a primary meridian and an
orthogonal secondary meridian, the model ophthalmic element comprising an
anterior surface and an opposing posterior surface, the model ophthalmic
element characterized by a higher order tonic shape imposed on one of the
surfaces, the higher order toric shape including a first profile disposed
along the primary meridian and a second profile disposed along the
secondary meridian that is different in shape from the first profile, the
higher order tonic shape being characterized by a profile along at least
one meridian that changes with increasing radius from the optical axis
raised to a power that is greater than two; providing a merit function
representative of the optical performance of a system including the model
cornea and the model ophthalmic element; selecting a value of a first
coefficient of an equation characterizing the higher order tonic shape of
the model ophthalmic element; calculating a value of the merit function
based on the value of the first coefficient and determining whether the
value of the merit function is above a predetermined value; repeating
selecting a value of the first coefficient and calculating a value of the
merit function until the merit function is above the threshold value; and
producing a physical ophthalmic element based on a value of the first
coefficient that causes the merit function to be above the threshold
value.

20. The method of claim 19, wherein providing a model cornea includes
providing corneal information, the corneal information being selected
from the group consisting of information of the shape of a cornea of a
particular eye and an average corneal shape of a population of eyes.

21. The method of claim 20, wherein the population of corneas includes
eyes having differing amounts of cylinder power.

22. The method of claim 21, wherein the differing amounts of cylinder
power range from less than or equal to 0.25 Diopter to greater than or
equal to 3 Diopters.

23. The method of claim 19, wherein providing the model ophthalmic
element is selected from the group consisting of producing an intraocular
lens, producing a corneal implant, producing a contact lens, and
performing a corneal surgical procedure.

24. The method of claim 19, wherein the asphericity of each meridian of
the first and second meridians is characterized by one or more of a conic
equation containing a curvature value and a conic constant; and a
polynomial equation including at least one term that changes according to
radius from a center of the model cornea raised to a power that is
greater than two.

25. The method of claim 19, wherein the method further comprises:
selecting a second coefficient of the equation characterizing the higher
order tonic shape of the model ophthalmic element; calculating a value of
the merit function based on the values of the first coefficient and the
second coefficient, and determining whether the value of the merit
function is above a predetermined value; repeating selecting values of
one or both of the first coefficient and the second coefficient, and
calculating a value of the merit function until the merit function is
above the threshold value; and providing a physical ophthalmic element
based on values of the first coefficient and the second coefficient that
cause the merit function to be above the threshold value.

27. The method of claim 19, wherein the corneal model is selected from
the group consisting of the shape of a cornea of a particular eye and an
average corneal shape of a population of eyes.

28. A system for producing an ophthalmic element, comprising: a memory
coupled to a processor, the memory comprising a plurality of code modules
for execution by the processor and one or more data values used during
execution of the code modules, the memory including: i) data for defining
a model cornea characterized by one or more of: an aspheric profile along
a first meridian of the model cornea that is different from an aspheric
profile along a second meridian of the model cornea; one or more of
fifth-order, seventh-order, and ninth-order aberrations; and an
asphericity of a first zone of the model cornea that is different from an
asphericity of a second zone of the model cornea surrounding the first
zone; ii) data for defining a model ophthalmic element disposed about an
optical axis comprising an anterior surface and an opposing posterior
surface, the model ophthalmic element characterized by a higher order
toxic shape imposed on one of the surfaces, the higher order tonic shape
including a first profile disposed along a primary meridian of the model
ophthalmic element and a second profile disposed along a secondary
meridian of the model ophthalmic element that is different in shape from
the first profile, the higher order tonic shape being characterized by a
profile along at least one meridian that changes with increasing radius
from the optical axis raised to a power that is greater than two; iii)
one or more code modules for calculating a merit function representative
of the optical performance of a system including the model cornea and the
model ophthalmic element; iv) one or more code modules for selecting a
value of a first coefficient of an equation characterizing the higher
order toric shape of the model ophthalmic element; v) one or more code
modules for calculating a value of the merit function based on the value
of the first coefficient and determining whether the value of the merit
function is above a predetermined value; vi) one or more code modules for
repeating selecting a value of the first coefficient and calculating a
value of the merit function until the merit function is above the
threshold value; and vii) one or more code modules for providing
parameters necessary to produce a physical ophthalmic element, the
parameter values being based on a value of the first coefficient that
causes the merit function to be above the threshold value; and an output
containing the parameters necessary to produce the physical ophthalmic
element

29. The system of claim 28, wherein the output includes one or more of a
monitor displaying values for the parameters, one or more sheets of paper
containing values for the parameters, and an electronic signal containing
values of the parameters readable by an electronic device.

Description:

BACKGROUND OF THE INVENTION

[0001] 1. Field of the Invention

[0002] The present invention relates generally to ophthalmic lenses, and
more specifically to toric ophthalmic lenses such as tonic contact
lenses, corneal inlays, and intraocular lenses.

[0003] 2. Description of the Related Art

[0004] Ophthalmic lenses, such as spectacles and contact lenses, may be
configured to provide both spherical and cylinder power. The cylinder
power of a lens is used to correct the rotational asymmetry aberration of
astigmatism of the cornea or eye, since astigmatism cannot be corrected
by adjusting the spherical power of the lens alone. Lenses that are
configured to correct astigmatism are commonly referred to as tone
lenses. As used herein, a toric lens is characterized by a base spherical
power (which may be positive, negative, or zero) and a cylinder power
that is added to the base spherical power of the lens for correcting the
astigmatism of the eye.

[0005] Tone lenses typically have at least one surface that can be
described by an asymmetric tone shape having two different curvature
values in two orthogonal axes, wherein the tonic lens is characterized by
a "low power meridian" with a constant power equal to the base spherical
power and an orthogonal "high power meridian" with a constant a power
equal to the base spherical power plus the cylinder power of the lens.
Intraocular lenses, which are used to replace or supplement the natural
lens of an eye, may also be configured to have a cylinder power for
reducing or correcting astigmatism of the cornea or eye.

[0006] In addition to astigmatism, the cornea or eye may also have other
higher order aberrations that can degrade optical quality or visual
acuity. For example, so called third order, or Seidel, aberrations also
include spherical aberration and coma, in addition to astigmatism. As
discussed in U.S. Patent Application Number 2009/0279048, which is herein
incorporated by reference in its entirety for all purposes as if fully
set forth herein, these additional higher order aberrations may be
reduced or corrected by introducing an aspheric surface or shape that is
characterized by a curvature and conic constant. The aspheric surface may
be on the same surface or opposite surface to that of the tonic shape.
Thus, the combination of the tone and aspheric shapes provides the
possibility of reducing or correcting all third order aberrations of lens
itself and/or of cornea or eye.

[0007] One problem that has yet to be implemented in to ophthalmic lens
design is that the cornea or eye may introduce even higher order
aberrations, for example, fifth-order, seventh-order, and ninth-order
aberrations. Furthermore, because the cornea may generally have an
asymmetric surface shape, the value of these aberrations may vary over
different meridians. However, it may be useful to approximate this
complexity of the typical cornea by characterizing the higher order
aberrations as having different values in orthogonal axes, for example,
along the high and low power meridians. While the magnitude of such
higher order aberrations may be relatively small compared to third-order
or Seidel aberrations, a clinically significant treatment may be provided
by correcting these aberrations. Fifth and higher order aberrations
cannot generally be reduces by ophthalmic lens surfaces characterized by
only a curvature and conic constant. Rather, additional lens or surface
design parameters are necessary.

[0008] Another problem within the art of ophthalmic lens design is that of
identifying average amounts of various aberrations within different
populations. Different cornea models have been developed that provide
average curvature and conic constant values for populations of human
eyes, for example, as disclosed in U.S. Pat. No. 6,609,793, which is
herein incorporated by reference in its entirety for all purposes as if
fully set forth herein. However, the average spherical aberrations within
such populations can vary depending on other variables such as the amount
astigmatism, axial length of the eye, average corneal curvature, age,
sex, ethnicity, and the like. For example, a subgroup within the
population all having about 1 Diopter of astigmatism may have a different
amount of spherical aberrations, on average, than another subgroup within
the population all having about 3 Diopters of astigmatism. In addition,
the average conic may be different between the high and low power
meridians, either for the population as a whole or for different
subgroups within the population having different amounts of astigmatism
or differentiated by some other parameter(s).

[0009] Yet another problem may occur in the case of subjects that have
previously undergone a corneal refractive procedure, such as LASIK or
PRK, and now need or desire to have the natural lens replaced by an
intraocular lens. In such cases, the corneal refractive procedure may
have been performed on only the central portion of the cornea, for
example, out to a diameter of 3 millimeters or 4 millimeters. The border
between the treated and untreated portions of the cornea may have
relatively discontinuous or large changes in curvature and/or power,
which in turn may introduce fifth and higher order aberrations that are
different from those in a typical population that has not received a
corneal refractive procedure.

[0010] For these and other reasons, there is a need for ophthalmic lenses,
and methods of design and implementation thereof; that take into account
fifth and higher order aberrations of individual, corneas and average
corneas representative of a population of eyes. There is also a need for
ophthalmic lenses, and methods of design and implementation thereof; that
take into account changes in the average aberrations of populations of
eyes over changes in certain parameters, such as differing amounts of
astigmatism.

BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Embodiments of the present invention may be better understood from
the following detailed description when read in conjunction with the
accompanying drawings. Such embodiments, which are for illustrative
purposes only, depict novel and non-obvious aspects of the invention. The
drawings include the following figures:

[0012] FIG. 1 is a perspective view of the anterior side of an ophthalmic
element according to an embodiment of the present invention.

[0013] FIG. 2 is a perspective view of the posterior side of the
ophthalmic element shown in FIG. 1.

[0014] FIGS. 3A and 3B are three dimensional and two dimensional plots of
an optic surface.

[0015] FIG. 4A and 4B are similar to FIGS. 3A and 3B, but also include
higher order polynomial terms.

[0016] FIG. 5A and 5B are similar to FIGS. 4A and 3B, but introduce a
third order polynomial term.

[0017] FIG. 6 is a flow chart illustrating a method of providing an
ophthalmic element according an embodiment of the present invention.

[0018] FIG. 7 is schematic diagram of a system for providing an ophthalmic
element according an embodiment of the present invention.

DETAILED DESCRIPTION OF THE DRAWINGS

[0019] Each and every feature described herein, and each and every
combination of two or more of such features, is included within the scope
of the present invention provided that the features included in such a
combination are not mutually inconsistent.

[0020] Embodiments of the present invention are generally directed to
tonic lenses or surface shapes, and/or related methods and systems for
fabrication and use thereof. Toric lenses according to embodiments of the
present invention find particularly use in or on the eyes of human or
animal subjects. Embodiments of the present invention are illustrated
below with particular reference to intraocular lenses; however, other
types of lenses fall within the scope of the present invention including,
but not limited to, contact lenses, spectacles, phakic intraocular
lenses, corneal inlays or onlays, corneal refractive procedures (e.g.,
LASIK (procedures), and the like.

[0021] Embodiments of the present invention include ophthalmic tonic
lenses and surfaces configured to reduce, or correct, astigmatism and at
least one other higher order monochromatic aberration of an individual,
average, and/or model cornea or eye. Tone lenses and surfaces according
to embodiments of the present invention include a cylinder power and at
least one surface comprising an asymmetric aspheric shape characterized
by a parameter or coefficient that affects or changes the aspheric shape
according to an independent variable (e.g., distance from a center or
optical axis) raised to a power that is greater than two, for example, to
a power that is greater than or equal to four. Compared to conventional
tonic lenses, tone lenses according to such embodiments of the present
invention advantageously enhance optic quality and/or visual acuity of
astigmatic corneas containing fifth and higher order aberrations.

[0022] In other embodiments, a tonic lens has an aspheric shape that
depends on, or is determined by, the amount of spherical and/or cylinder
power of the toric lens. For example, the aspheric shape of the tone lens
may be characterized by conic equation, where the value of the conic
constant depends on the cylinder power of the lens. In this case, a
population of subjects having an astigmatism approximately equal to the
cylinder power of the tonic lens have an optical performance or visual
acuity that is enhanced in comparison to that provided by a similar tone
lens having no aspheric shape, or in comparison to a similar toric lens
having an aspheric shape is independent of the cylinder power of the
lens. Additionally or alternatively, the tonic lens has an aspheric shape
that depends on, or is determined by, some other optical parameter of the
toric lens.

[0023] As used herein, the term "clear aperture" or "optical zone" means
the area of a lens or optic defining the extent of the lens or optic
available for forming an image or focus from a collimated or distant
light source. The clear aperture or optical zone is usually circular and
specified by a diameter. The clear aperture or optical zone may have the
same or substantially the same diameter as the optic or lens itself.
Alternatively, the diameter of the clear aperture or optical zone may be
smaller than the diameter of the optic, for example, due to the presence
of a glare or PCO reducing structure that is disposed about a peripheral
region of the optic.

[0024] As used herein, the term "optical power" means the ability of a
lens or optic, or portion thereof, to converge or diverge light to
provide a focus (real or virtual), and is commonly specified in units of
reciprocal meters (m.sup.-) or Diopters (D). When used in reference to an
intraocular lens, the term "optical power" means the optical power of the
intraocular lens when disposed within a media having a refractive index
of 1.336 (generally considered to be the refractive index of the aqueous
and vitreous humors of the human eye), unless otherwise specified. See
ISO 11979-2, which is herein incorporated by reference in its entirety
for all purposes as if fully set forth herein. As used herein the term
"focal length" means the reciprocal of the optical power. As used herein
the term "power", when used in reference to an optic or lens, means
"optical power". As used herein, the term "refractive power" or
"refractive optical power" means the power of a lens or optic, or portion
thereof, attributable to refraction of incident light. As used herein,
the term "diffractive power" or "diffractive optical power" means the
power of a lens or optic, or portion thereof, attributable to diffraction
of incident light into one or more diffraction orders. Except where noted
otherwise, the optical power of a lens or optic is from a reference plane
associated with the lens or optic (e.g., a principal plane of an optic).

[0025] As used herein, the terms "about" or "approximately", when used in
reference to a Diopter value of an optical power, mean within plus or
minus 0.25 Diopter of the referenced optical power(s). As used herein,
the terms "about" or "approximately", when used in reference to a
percentage (%), mean within plus or minus one percent (±1%). As used
herein, the terms "about" or "approximately", when used in reference to a
linear dimension (e.g., length, width, thickness, distance, etc.) mean
within plus or minus one percent (1%) of the value of the referenced
linear dimension.

[0026] Referring to FIGS. 1 and 2, in certain embodiments, a foldable
intraocular lens 10 comprises an optic or optic body 11 including a clear
aperture or optical zone 12 and a peripheral zone 13 entirely surrounding
optical zone 12. Optic 11 has an anterior surface 14, a substantially
opposing posterior surface 18, an optic edge 20, and an optical axis 22.
Optic 11 includes a primary meridian and a secondary meridian that is
perpendicular to the primary meridian. Anterior surface 14 comprises a
central face 24, a peripheral face 28, and a recessed annular face 30
therebetween that is disposed posterior to peripheral face 28.
Intraocular lens 10 further comprises haptics 32 (32a, 32b) extending
from optic 11 that may optionally be integrally formed with optic 11.

[0027] In some embodiments, intraocular lens 10 is a tonic intraocular
lens that includes a base toric shape imposed on or added to at least one
of surfaces 14, 18. In such embodiments, the base tonic shape includes a
low power meridian having a low optical power and a high power meridian
having a high optical power equal to the low optical power plus a
cylinder optical power. The high power meridian may be disposed along the
primary or secondary meridian, or may be a some angle between the primary
and secondary meridians, for example, and a 45 degree angle from the
primary or secondary meridian. In the illustrated embodiment, intraocular
lens 10 also comprises a first mark 42a and a second mark 4b, which may
be configured for use in angularly aligning toric intraocular lens 10 in
the eye and are disposed along, or form, an imaginary line 44 when viewed
from anterior side 14 or posterior side 18 of intraocular lens 10.

[0028] A detailed description of various elements and features of
intraocular lens 10, as shown in FIGS. 1 and 2, may be found in U.S.
Patent Application Publication 2005/0125056 and U.S. patent application
Ser. No. 12/620,765, both of which are herein incorporated by reference
in their entirety for all purposes as if fully set forth herein. Various
structural features of intraocular lens 10 shown in FIGS. 1 and 2 are
exemplary, and other optic body and haptic structures are within the
scope of embodiments of the present invention.

[0029] In the illustrated embodiment, optic 11 is commonly circular and
may be constructed of at least one of the materials commonly used for
resiliently deformable or foldable optics, such as silicone polymeric
materials, acrylic polymeric materials, hydrogel polymeric materials,
such as polyhydroxyethylmethacrylate, polyphosphazenes, polyurethanes,
and mixtures thereof and the like. Alternatively, optic 11 may be
constructed of at least one of the commonly employed material or
materials used for rigid optics, such as polymethylmethacrylate (PMMA).
In some embodiments, optic 11 is made of SENSAR® brand of acrylic.
Other advanced formulations of silicone, acrylic, or mixtures thereof are
also anticipated. Optic 11 material may be selected such that optical
zone 12 is optically clear and exhibits biocompatibility in the
environment of the eye. Foldable/deformable materials are particularly
advantageous since optics made from such deformable materials may be
rolled, folded or otherwise deformed and inserted into the eye through a
small incision. The lens material may have a refractive index provides a
relatively thin, flexible optic section, for example, having a center
thickness that is from 150 micrometers to 1000 micrometers, depending on
the material and the base optical power of optic 11. For example, in one
embodiment, optic 11 is made of Sensar® brand of acrylic and a base
optical power of 20D. In such embodiment, optic 11 has a center thickness
Tc that may be from 0.4 millimeter to 1.5 millimeter. The center
thickness Tc may vary from this range, depending on factors such as
the lens material and the dioptric power of optical zone 12, or the use
of diffractive surfaces or profiles. Optic 11 may have a diameter that is
from 4 millimeters to 8 millimeters, or more. As used herein the term
"thickness", when used in reference to lens or optic, generally refers to
a dimension in a direction that is along, or substantially along, an
optical axis about which the lens or optic is disposed.

[0030] Intraocular lens 10 may comprise any of the various means available
in the art for centering or otherwise locating or supporting optical zone
12 within the eye. In the illustrated embodiment haptics 32 are used for
centering intraocular lens 10 within the eye; however, other types of
support structure may be used, for example, as typically used for
supporting an optic or optics of an accommodating intraocular lens.
Haptics 32 of the illustrated embodiment may be integrally formed of the
same material as optic 11 to faun a one-piece IOL. Alternatively, haptics
32 may be integrally formed in a common mold with optic 11, but be made
of a different material than optic 11. In other instances, haptics 32 is
&mined of the same material as optic 11, but haptics 32 and optic 11
materials have different states, for instance differing amounts of water
content or percentage of a cross-linked polymer. Additionally or
alternatively, haptics 32 may be formed separately from optic 11 and
subsequently attached to optic 11 to provide a three-piece configuration.
Haptics 32 may comprise any of a variety of materials which exhibit
sufficient supporting strength and resilience, and which are
substantially biologically inert in the intended in vivo or in-the-eye
environment. Suitable materials for this purpose include, for example,
polymeric materials such as polypropylene, PMMA, polycarbonates,
polyamides, polyimides, polyacrylates, 2-hydroxymethylmethacrylate, poly
(vinylidene fluoride), polytetrafluoroethylene and the like; and metals
such as stainless steel, platinum, titanium, tantalum, shape-memory
alloys, e.g., nitinol, and the like. In other embodiments, intraocular
lens 10 comprises a positioning means that allows optic 11 to move along
optical axis 22 or be deformed in response to deformation of the capsular
bag and/or in response to the ciliary muscles of the eye.

[0031] Optical zone 12 may include various forms suitable for providing
vision to a subject. For example, optical zone 12 may be biconvex,
plano-convex, plano-concave, meniscus, or the like. The base optical
power of optical zone 12 may be either positive or negative. The general
shape of posterior surface 18 and central face 24 of anterior surface 14
may include any shape generally used for producing an optic portion
configured to focus, or form an image from, light incident on the optic.
For instance, one of surfaces 14, 18 may be spherical with an overall
radius of curvature that is either positive or negative. The shape of at
least one of surfaces 14, 18 is aspheric, as discussed in greater detail
below herein. One or both surfaces 14, 18 may be optionally configured to
provide more than one focus, for example to correct for both near and
distant vision as described by Portney in U.S. Pat. No. 4,898,461.
Optical zone 12 may be configured as part of a lens system (e.g., a two
optic system) and/or for providing accommodative vision (e.g., by being
made of a material that can change shape to provide varying base optical
power in response to an ocular force).

[0032] At least portions of posterior surface 18 and/or central face 24 of
optical zone 12 may comprise one or more optical phase plates. In such
embodiments, the total base optical power of optical zone 12 is a
combination of the base refractive power of posterior surface 18 and
central face 24, and the diffractive optical power of the one or more
diffraction orders produced by the one or more phase plates. The one or
more phase plates may be either a monofocal phase plate providing one
dominant diffraction order or a multifocal phase plate, such as a bifocal
phase plate, for providing, for instance, simultaneous near and distant
vision. Other types of phase plates may also be used. For example, the
phase plate may be based on a change in the refractive index of the
material used to form optical zone 12.

[0033] The total base optical power of optical zone 12 may be from +2
Diopters to +50 Diopters, or more, commonly within a range of +5 Diopters
to +40 Diopters, or a range of +5 Diopters to +30 Diopters. The total
base optical power of optical zone 12 may be either positive or negative,
for instance within a range of -15 Diopters or to +50 Diopters or more,
or within a range of -10 Diopters to +40 Diopters. Other ranges of
refractive optical power may be preferred, depending on the particular
application and type of intraocular lens to be used. As discussed above
herein, when referring to an intraocular lens, the base powers discussed
in this paragraph generally refer to the optical power of the intraocular
lens when disposed within a surrounding media having a refractive index
of 1.336.

[0034] At least one of surfaces 14, 18 includes a higher order toric shape
imposed on, added to, or combined with one of surfaces 14, 18. The higher
order toric shape is non-axisymmetric so that optic 11 may be configured
reduce or correct ocular aberrations that are not treated using prior art
lenses. As used herein, the term "non-axisymmetric", when applied to a
surface shape or profile, means a surface in which the shape or profile
various meridians through the optical axis of the surface is different
and/or depends on the angle of the meridian relative to a reference
meridian or axis. The base tone shape and the higher order toric shape
may be disposed on opposite surfaces of surfaces 14, 18. Alternatively,
the base toric shape and the higher order tonic shape may both be
disposed on a same surface 14 or 18. The higher order toric shape is
characterized by a profile along at least one meridian that changes with
increasing radius from the optical axis raised to a power that is greater
than two, for example, is characterized by a profile along at least one
meridian that changes with increasing radius from the optical axis raised
to a fourth, sixth, and/or higher power. As used herein the "order" or
"power" of a polynomial term within a polynomial equation is the sum of
the powers of each independent variable within the polynomial term. In
the case of polynomial having two independent variables (e.g., x and y
along axes perpendicular to an optical axis), the "order" or "power" of a
polynomial term is the sum of the powers of the x and y variable within
the polynomial term. For example, profiles that change with increasing
radius from the optical axis raised to a fourth power include surfaces
described by terms including x4, y4, x2y2, xy3,
x3y, where x and y are coordinate along two axes of optic zone 12
that are perpendicular to an optical axis of optic zone 12 (e.g., a
z-axis). Examples of profiles that change with increasing radius from the
optical axis raised to a sixth power include surfaces described by terms
including x6, y6, x2y4, x4y2,
x3y3, and the like.

[0035] Advantageously, the non-axisymmetric characteristics of the higher
order tonic shape may be configured to reduce fifth-order and/or higher
optical aberrations of a cornea or eye into which tonic intraocular lens
10 is placed. Additionally or alternatively, the non-axisymmetric
characteristics of the higher order toric shape may be configured so that
optic zone 12 reduces a fifth-order or higher optical aberration of an
average cornea or eye of a particular population of eyes. In certain
embodiments, intraocular lens 10 does not include the base toric shape,
for example, in cases where the cornea being corrected has higher order
aberrations that are non-axisymmetric, but no astigmatism or an
astigmatism that is less than or equal to 0.25 Diopters or is less than
or equal to 0.5 Diopters.

[0036] The overall shape of an optic surface containing the base toric
shape and/or the higher order tonic shape may be regarded as the
superposition of either or both tonic shapes with a surface shape of that
optic surface. The base surface shape may be planer or spherical and
characterized by a constant curvature or radius of curvature.
Alternatively, the base surface may have an axisymmetric aspheric shape,
for example, configured to reduce a symmetrical third order aberration of
optic zone 12 and/or of an eye into which intraocular lens 10 is to be
placed. Additionally or alternatively, the aspheric base surface may be
configured to provide some other optical effect, for example, to provide
an increased or enhanced depth of focus or to provide a multifocal lens
(either refractive or diffractive).

[0037] In some embodiments, the base tonic shape and/or the higher order
tonic shape is located on one of surfaces 14, 18, while the opposite
surface 18, 14 includes axisymmetric aspheric shape (e.g., to reduce a
spherical aberration of the lens 10 or eye, provide an increased depth of
focus, and/or provide a multifocal lens). Alternatively, the base toric
shape and/or the higher order tonic shape may be combined with or added
to the axisymmetric aspheric shape on a single surface of optic zone 12.

[0038] In certain embodiments, the axisymmetric aspheric shape may be
characterized by a conoid of rotation, wherein a surface sag profile
along any meridian varies according to the equation:

z = cr 2 1 + 1 - ( 1 + k ) c 2 r 2 ( 1 )
##EQU00001##

where z is the surface sag along a z-axis, r is the radial distance from
the optical axis 22, c is a base curvature of the surface (which is equal
to 1/R, where R is the radius of curvature), and k is a conic constant of
the surface. Alternatively, at least one of the surfaces of intraocular
lens 10 may be characterized by a modified conoid of rotation, wherein
the surface sag profile along any meridian varies according to the
relation:

where a2,a4, . . . are constants, c is a base curvature of the
surface (which is equal to 1/R, where R is the radius of curvature, k is
a conic constant, and r is the radial distance from the optical axis 22.
For Equations 1 and 2, as well as for other embodiments discussed below,
the z-axis may be parallel to optical axis 22. Alternatively, the z-axis
may have an offset angle from the optical axis 22.

[0039] In some embodiments, a surface sag profile of at least one of
surfaces 14, 18 is characterized by the equation:

where x and y are coordinate values along an x-axis and a y-axis,
respectively, z is a surface sag coordinate value along a z-axis
perpendicular to the x and y axes, r2 is equal to x2+y2, c
is a base curvature, k is a conic constant, and A20, A11,
A02, A40, A04, A22, A60, A06, A42, and
A24 are polynomial coefficients of the equation. The coefficients
A20, A11, A02 may be used to characterize the base toric
shape, while the coefficients A40, A04, A22, A60,
A06, A42, and A24 may be used to characterize the higher
order tonic shape. Since the polynomial in Equation (3) includes
polynomial terms containing both x and y variables, the polynomial
coefficients may be selected so that the higher order tonic shape is
non-axisymmetric. Thus, the higher order toric shape may be configured so
that the profile along various meridians change or vary with angle
relative to a reference axis (e.g., the x-axis or y-axis). For example, a
non-axisymmetric higher order tonic shape may be defined when A40 is
unequal to A04, when A60 is unequal to A06, or when
A22, A42, and/or A24 have non-zero values. Advantageously,
the non-axisymmetric form of the higher order tonic shape make more
design variables available for reducing fifth and higher order corneal
aberrations than does an axisymmetric shape, the latter being
characterized by polynomial terms having only one independent variable
(e.g., radius r from optical axis 22). The additional fourth and sixth
order design variables aid, for example, in reducing fifth and higher
order aberrations--especially asymmetric fifth and higher order
aberrations. Such aberrations cannot be adequately reduced using optical
elements that only include a spherical power and tonic power oriented
along a particular meridian, even when incorporating one or more conic
constants for reducing third order aberrations such as lower order
spherical aberrations. The polynomial portion of Equation (3) may also
contain additional higher order terms (e.g., terms including x8,
y8, x6y2, x2y6, x4y4, x10, and
the like) as desired for reducing or balancing even higher order corneal
aberrations. In certain embodiments, a polynomial surface profile or
shape has one or more eighth and/or sixteenth order polynomial
terms--either alone or in combination with other higher order terms--that
are configured or selected to reduce or modify fourth or fifth order
aberrations, respectively, of an incident wavefront.

[0040] Alternatively, if intraocular lens 10 is used a cornea having
higher order aberrations, but no or little astigmatism, the surface sag
profile of at least one of surfaces 14, 18 is characterized by the
equation:

where x and y are coordinate values along an x-axis and a y-axis,
respectively, z is a surface sag coordinate value along a z-axis
perpendicular to the x and y axes, r2 is equal to x2 +y2,
c is a base curvature, k is a conic constant, and A40, A04,
A22, A60, A06, A42, and A24 are polynomial
coefficients of the equation, which may be selected to characterize the
higher order toric shape of lens surface 14 and/or 18.

[0041] All of the options and combinations discussed above are available
to a designer through use of the surface definition provided by Equations
(3) and (4). This gives designers great flexibility in reducing,
compensating for, and/or balancing both third order and higher order
corneal aberrations, particularly in the case of asymmetric or
non-axisymmetric higher order aberrations.

[0042] In another alternative to Equation (3), a surface sag profile of at
least one of surfaces 14, 18 may be characterized by the equation:

where x and y are coordinate values along an x-axis and a y-axis,
respectively, z is a surface sag coordinate value along a z-axis
perpendicular to the x and y axes, r2 is equal to x2 +y2,
where c1 is the base curvature along a first meridian of optic body
11, k1 is the conic constant along the first meridian, c2 is
the base curvature along a second meridian of optic body 11, k2 is
the conic constant along the second meridian, and A40, A04,
A22, Aho, A06, A42, and A24 are polynomial
coefficients of the equation. The coefficients c1 and c2 may be
used to characterize the base tonic shape, while the coefficients
A40, A04, A22, A60, A06, A42, and A24
may be used to characterize the higher order tonic shape. The two conic
constant coefficients k1 and k2 may be used to independently
introduce differing amounts of third order aberration along two
orthogonal axis of intraocular lens 10. Similar to Equation (2), the
polynomial in Equation (3) includes polynomial terms containing both x
and y variables, so that the coefficients may be selected to make the
higher order toric shape non-axisymmetric. For example, a
non-axisymmetric higher order tonic shape may be defined when A40 is
unequal to A04, when A60 is unequal to A06, or when
A22, A42, and/or A24 have non-zero values.

[0043] In certain embodiments, the surface sag profile of at least one of
surfaces 14, 18 includes polynomial terms in which x and/or y are raised
to an odd valued power (e.g., 1, 3, and/or 5). Such odd valued power
terms provide a surface having a shape that is not only asymmetric in the
sense that the profile or shape along different meridians changes with
angular orientation about the optical axis, but is also asymmetric along
one or more individual meridians. That is, for a surface characterized by
a polynomial term having an odd valued power variable (e.g., x, or y in
the above equations), at least one meridian of the surface will have a
shape or profile that is different on each side of the optical axis.

[0044] Referring to FIGS. 3-5, various shape and profile features of
surfaces according to embodiments of the invention will now be discussed.
The plots shown in FIGS. 3-5 are based on the equation::

[0045] The base surface in these examples is spherical (i.e., the conic
constant, k, is equal to zero). The plots are based on an aperture having
a diameter of 1 arbitrary unit. The vertical axis is also in arbitrary
units and the scale is exaggerated to demonstrate the features of each
design. The coefficient values for each plot are shown in Table 1. In
discussing these figures, the x-axis will be referred to as the primary
meridian and the y-axis will be referred to as the secondary meridian.

[0046] Referring to FIGS. 3A and 3B, a standard toric surface is shown in
which the primary meridian (x-axis) has a higher optical power than the
secondary meridian. FIG. 3A shows a three dimensional plot of the surface
shape, while FIG. 3B shows a two-dimensional plot of the surface profiles
along the primary and secondary axes. As seen in FIG. 3B, each profile
has a parabolic shape imposed on or added to a base spherical surface
having a curvature of 2.

[0047] FIGS. 4A and 4B show the same type plots as those in FIGS. 3A and
3B, but the standard tonic shape (defined by A.20 and A.02) is replace
with two fourth order terms. As seen in FIG. 4B, the slope near the
center along the two profiles is less near the center than in the case of
FIG. 3B. However, the slope increases more rapidly at the periphery in
FIG. 4B than in FIG. 3B. The surface in FIGS. 4A and 4B also has the same
base spherical shape, and thus illustrate a spherical surface that is
influenced more by the fourth order terms as the radius from the center
of the surface increases. Such a surface may be suited for correction
aberrations of a generally spherical cornea, but which has higher order
spherical aberrations. A base toric surface like than shown in FIGS. 3A
and 3B may also be added to the surface in FIGS. 4A and 4B, which would
additional correct for a lower order astigmatism of the cornea.

[0048] FIGS. 5A and 5B are similar to those shown in FIGS. 4A and 4B;
however, an asymmetric third order term has been introduced along the
secondary meridian. While the primary meridian is still symmetric about
the center, the secondary meridian is clearly asymmetric about the center
of the surface. Such a surface may be well suited to correct both coma
and higher order astigmatisms.

[0049] Referring to FIG. 6, a method 100 may be used to provide an
ophthalmic element according an embodiment of the present invention. The
method 100 may be used, for example, to provide various embodiments of
the intraocular lens 10 discussed above. Alternatively, method 100 may be
used to provide other ophthalmic lenses such as corneal implants, contact
lenses, spectacles, or the like.

[0050] Using the intraocular lens 10 as an example, method 100 comprises
an element 110 that includes providing a model cornea. Method 100 also
comprises an element 120 that includes providing a model ophthalmic
element according to an embodiment of the present invention. Method 100
additionally comprises an element 130 that includes providing a merit
function representative of the optical performance of a system including
the model cornea and the model ophthalmic element. Method 100 also
comprises an element 140 that includes selecting a value of one or more
coefficients of an equation characterizing the higher order toric shape
of the model ophthalmic element. Method 100 further comprises an element
150 that includes calculating a value of the merit function based on the
value of the one or more coefficients, and an element 160 that includes
determining whether the value of the merit function is above a
predetermined value. Method 100 further comprises an element 170 that
includes producing a physical ophthalmic element based on a value of the
one or more coefficients that causes the merit function to be above the
threshold value.

[0051] Element 110 of method 100 includes providing the model cornea. The
model cornea may be a physical model of the cornea of a human or animal
eye, wherein the model cornea is part of a system that also contains at
least one light sources and an electronic or photographic detector that
may be used to evaluate images formed by the model cornea. Alternatively,
the model cornea may comprise various parameters of an optical program or
electronic model utilized to calculate or evaluate the optical
performance of the cornea in conjunction with an ophthalmic element
according to an embodiment of the present invention. In either case, the
model cornea may be characterized by various parameters or features that
produce aberrations to be corrected or reduced by an ophthalmic element
such as the intraocular lens 10. For example, the model cornea may be
characterized an aspheric profile along a first meridian of the model
cornea that is different from an aspheric profile along a second meridian
of the model cornea. Additionally or alternatively, the model cornea may
be characterized by higher order aberration, for example, a fifth-order
aberration, seventh-order aberration, and/or ninth-order aberration.
Additionally or alternatively, the model cornea may be characterized by
an asphericity of a first 1.5 zone of the model cornea that is different
from an asphericity of a second zone of the model cornea surrounding the
first zone. Such a model cornea may be used simulate or evaluate corneas
which have undergone a refractive surgical procedure.

[0052] In certain embodiments, element 110 additionally or alternatively
includes providing an eye model, of which the model cornea may be a part.
For example, the model cornea may incorporate average characteristics or
values of parameters characterizing the corneas of people or animals over
a certain age, people or animals that are candidates for a surgical
procedure (e.g., a cataract and/or corneal refractive procedure), people
or animals that are that have an astigmatism, or correction cylinder
power, falling within a certain range and/or offset angle (e.g., an
astigmatism, or correction cylinder power, between 0.5 and 1.5 Diopters,
between 1.5 and 2.5 Diopters, between 1.5 and 3 Diopters, or greater than
3 Diopter or 4 Diopters), and the like. The eye model may take into
account physical and optical characteristics for a given population. For
example, the eye model may be based on the Navarro eye model, as
disclosed in "Accommodation-dependent model of the human eye with
aspherics", J. Opt. Soc. Am. A, Vol. 2, No. 8, pp. 1273-1281, which is
herein incorporated by reference in its entirety for all purposes as if
fully set forth herein. Alternatively, the eye model may be one of those
disclosed in U.S. Pat. Nos. 6,609,793 or 7,377,640, which are herein
incorporated by reference in their entirety for all purposes as if fully
set forth herein. In some embodiments, the model cornea is characterized
by Equations (1) or (2) above, where the pupil has a 5 millimeter
diameter, the model cornea has a radius of curvature of 7.553 millimeters
and a conic constant of -0.1034, and the eye has a refractive index
1.3375, as disclosed in U.S. Pat. Nos. 6,609,793. Rather than being based
on average values from a population, element 110 may provide a model
cornea or eye model that is based on optical and/or physical measurements
of an individual human or animal eye, wherein a custom ophthalmic element
may be provided.

[0053] Element 120 of method 100 includes providing a model ophthalmic
element, for example, an embodiment of the intraocular lens 10 discussed
above. The model ophthalmic element may be characterized by a higher
order toric shape that is imposed on, or added to, a surface of the model
ophthalmic element. The higher order toric shape includes a primary
meridian characterized by a first profile and a secondary meridian
characterized by a second profile that is different from the first
profile. The higher order tonic shape may be characterized by a profile
along at least one meridian that changes according to radius from the
optical axis raised to a power that is greater than two.

[0054] Element 130 of method 100 includes providing a merit function
representative of the optical performance of a system including the model
cornea and the model ophthalmic element. The merit function may
incorporate, or be based on, the performance of a lens, optic, surface,
or system that is defined, expressed, or quantified as an MTF that is
above a predetermined threshold value (e.g., 0.05, 0.10, 0.15, 0.17,
0.20, 0.25, or higher) at a particular frequency (e.g., 25, 50, or 100
line pairs per millimeter). As expressed herein, the performance of a
lens, optic, or surface according to embodiments of the present invention
may be expressed or quantified in terms of through-focus MTF data at a
particular spatial frequency. For example, the depth of focus may be
defined as the region in a through-focus plot over which the Modulation
Transfer Function (MTF) at a spatial frequency of 50 line pairs per
millimeter exceeds a selected cutoff value. Typical cutoff values may
include 0.05, 0.10, 0.15, 0.17, 0.20, 0.25, or higher. Other spatial
frequencies may include 25 line pairs per millimeter or 100 line pairs
per millimeter. Another way to define the depth of focus is based on a
relative threshold, where the threshold is defined based on a peak value
of a figure of merit. For instance, the depth of focus may be defined as
the full width at half max (FWHM) of the MTF at a particular spatial
frequency. Other relative thresholds may be 95%, 90%, 80%, 70%, 60%, 50%,
1/e, 1/e 2 of a peak value of the MTF, or any suitable fraction of the
peak value of MTF or another metric.

[0055] The performance of a lens, optic, surface, or system may be
defined, expressed, or quantified as an MTF performance over a range of
focal length, for example, to provide a lens having an extended or
enhanced depth of focus compared to another lens that is similar, but
does not incorporate features or elements of a lens configured according
to an embodiment of the present invention. The performance may be over a
defocus range expressed in terms of object space distances, image space
distances, or Diopter power. In some embodiments, a lens, optic, or
surface may be specified in terms of an increase in depth of focus as
compared to the corresponding reference optic, either in absolute terms
(e.g., an increased defocus range compared to the reference optic over
which a predetermined MTF performance is maintained) or in relative terms
(e.g., a percent increase in defocus range as compared to a reference
optic, such as a 10%, 20%, 50%, 100%, 200%, or greater increase in
defocus range as compared to a reference optic).

[0056] Additionally, performance of a lens, optic, surface, or system may
be defined, expressed, or quantified in terms of an axial distance, or,
equivalently, in terms of a power. The figures of merit, or metrics, may
be either purely optical in nature, or may incorporate some perception
effects from the human eye. For instance, any or all of the following
optical metrics may be used: MTF at a particular spatial frequency, MTF
volume (integrated over a particular range of spatial frequencies, either
in one dimension or in two dimensions), Strehl ratio, encircled energy,
RMS spot size, peak-to-valley spot size, RMS wavefront error,
peak-to-valley wavefront error, and edge transition width. Additionally
or alternatively, any of the following psychophysical metrics may be
used: contrast sensitivity, visual acuity, and perceived blur.
Additionally or alternatively, other metrics found in the literature may
be used, such as those detailed in Marsack, J. D., Thibos, L. N. and
Applegate, R. A., 2004, "Metrics of optical quality derived from wave
aberrations predict visual performance," J Vis, 4 (4), 322-8; Villegas,
E. A., Gonzalez, C., Bourdoncle, B., Bonnin, T. and Artal, P., 2002,
"Correlation between optical and psychophysical parameters as a function
of defocus," Optom Vis Sci, 79 (1), 60-7; van Meeteren, A., "Calculations
on the optical transfer function of the human eye for white light,"
Optica Acta, 21 (5), 395-412 (1974), all of these references being herein
incorporated by reference in its entirety for all purposes as if fully
set forth herein.

[0057] Any or all of the above performance definitions or criteria may be
characterized at a single wavelength, such as 550 nm or any other
suitable wavelength, at a plurality of selected wavelengths, or over a
spectral region, such as the visible spectrum from 400 nm to 700 nm. The
performance metrics may be weighted over a particular spectral region,
such as the weighting associated with the spectral response of the human
eye. It will be appreciated that the above criteria may be used in
determining or comparing the performance of any of the optic discussed
herein.

[0058] Element 140 of method 100 includes selecting a value of one or more
coefficients or parameters of an equation characterizing the higher order
toric shape imposed on a surface of the model ophthalmic element.
Alternatively, the value of parameters may be selected that are
representative of other shapes imposed on the same, or a different,
surface of the model ophthalmic element, either independently or in
conjunction with the coefficients for the higher order toric shape. For
example, parameters of one or more of Equations (1) through (5) may be
selected.

[0059] Once a merit function has been determined and coefficient values of
an equation characterizing the ophthalmic element have been selected,
element 150 of method 100 includes calculating a value of the merit
function based on initial value(s) of the coefficient(s) or parameter(s).
Element 160 includes deteimining whether the value of the merit function
is above a predetermined or threshold value. If the merit function is not
above the predetermined or threshold value, then elements 140 and 150 are
repeated wherein one or more coefficient or parameter values are changed.
Once as set of coefficients or parameter provide a merit function value
that is above the selected threshold or predetermined value, the element
170 of method 100 includes producing a physical ophthalmic element based
on the value of the first coefficient. The physical ophthalmic element
may be an intraocular lens such as an embodiment of intraocular lens 10
discussed above. Alternatively, the physical ophthalmic element may be a
spectacle lens, a contact lens, a corneal implant, or the like.
Additionally or alternatively, the physical ophthalmic element may
include a modification of the natural, for example, a corneal refractive
procedure such as a LASIK or PRK procedure on the cornea on an eye.

[0060] As used herein, a merit function for an optical element or system
is "above a threshold value" or "above a predetermined value" when the
optical element or system has a more favorable or desirable optical
performance than it would have if the optical element or system were
modified to have a merit function equal to the threshold or predetermined
value. For example, the "threshold value" of an optical system may be
selected to be an MTF 0.2 at a frequency of 50 line pairs per millimeter.
In this case, the system merit function would be "above the threshold
value" if the actual or calculated system MTF were greater than 0.2
(e.g., if the system had an MTF of 0.21, 0.25, or 0.3 at 50 line pairs
per millimeter), since a higher MTF is commonly considered to represent
better optical system performance. In another example, the "threshold
values" of an optical system may be selected to be an image spot diameter
of 20 micrometers. In this case, the system merit function would be
"above the threshold values" if the actual or calculated system image
spot diameter were less than 20 micrometer (e.g., if the system produced
a spot diameter of 18 micrometers or 10 micrometers), since a smaller
spot diameter is commonly considered to represent better optical system
performance. These two examples demonstrate that a particular merit
function may represent better optical performance as the value of the
merit function increases in value, or as the value of the merit function
decreases in value, depending on the units of the merit function.

[0061] Referring to FIG. 7, in certain embodiments of the present
invention, a system 200 for producing an ophthalmic element comprises an
electronic memory 202 coupled to a processor 205. Memory 202 includes a
plurality of code modules 208 for execution by processor 205 and one or
more data values 210 used during execution of code modules 208. The data
values 210 may include data values for defining a model cornea and for
defining a model ophthalmic element that are used in determining
parameters suitable for providing an ophthalmic element according to one
or more embodiments of the present invention. System 200 may further
include an input 212, for example, to provide data values 210 and/or at
least portions of code modules 208. System 200 may also include an output
215 that includes parameters suitable for use in fabricating or realizing
a physical ophthalmic element. In certain embodiments, the processor 205
is used carry out all or portions of method 100 discussed above and shown
in FIG. 6.

[0062] The processor 205 may be any electronic chip or circuit suitable
for making calculating necessary to provide an ophthalmic element
according to one or more embodiments of the present invention. Although
not required, the processor 205 and electronic memory 202 will commonly
be integrated into a single system such as a desktop or portable
computer, or some other specialized electronic system.

[0063] Data values 210 of memory 202 for defining the model cornea may
include, but is not limited to, one or more of: [0064] Data for an
aspheric profile along a first meridian of the model cornea that is
different from an aspheric profile along a second meridian of the model
cornea. [0065] Data for one or more of fifth-order, seventh-order, and
ninth-order aberrations. [0066] Data for an asphericity of a first zone
of the model cornea that is different from an asphericity of a second
zone of the model cornea surrounding the first zone. In the last
instance, the first zone may be or represent the area of an individual
cornea or average cornea over which a corneal refractive procedure has
been performed, while the second zone may be an area of the cornea that
is unaffected by the corneal refractive procedure.

[0067] Data values 210 of memory 202 for defining the model ophthalmic
element comprising an anterior surface and an opposing posterior surface,
wherein the model ophthalmic element is characterized by a higher order
tonic shape imposed on one of the surfaces, the higher order tonic shape
including a primary meridian characterized by a first profile and a
secondary meridian characterized by a second profile that is different
from the first profile, the higher order toric shape being characterized
by a profile along at least one meridian that changes according to radius
from the optical axis raised to a power that is greater than two.

[0068] Code modules 208 may include, but not limited to: [0069] One or
more code modules for calculating a merit function representative of the
optical performance of a system including the model cornea and the model
ophthalmic element; [0070] One or more code modules for selecting a value
of a first coefficient of an equation characterizing the higher order
toric shape of the model ophthalmic element; [0071] One or more code
modules for calculating a value of the merit function based on the value
of the first coefficient and determining whether the value of the merit
function is above a predetermined value. [0072] One or more code modules
for repeating selecting a value of the first coefficient and calculating
a value of the merit function until the merit function is above the
threshold value. [0073] One or more code modules for providing parameters
necessary to produce a physical ophthalmic element, the parameter values
being based on a value of the first coefficient that causes the merit
function to be above the threshold value.

[0074] Output 215 may include one or more of a monitor displaying values
for the parameters, one or more sheets of paper containing values for the
parameters, and an electronic signal containing values of the parameters
that are readable by a receiving electronic device used in providing the
ophthalmic element. For example, the receiving electronic device may be a
computer or processor that is used to calculate a treatment plan for
controlling a laser during a corneal refractive procedure. Alternatively,
the receiving electronic device may be a computer or processor that is
used to control, or provide input to, a machine used to produce an optic
element or a mode used to produce an optical element.

[0075] The above presents a description of the best mode contemplated of
carrying out the present invention, and of the manner and process of
making and using it, in such full, clear, concise, and exact terms as to
enable any person skilled in the art to which it pertains to make and use
this invention. This invention is, however, susceptible to modifications
and alternate constructions from that discussed above which are fully
equivalent. Consequently, it is not the intention to limit this invention
to the particular embodiments disclosed. On the contrary, the intention
is to cover modifications and alternate constructions coming within the
spirit and scope of the invention as generally expressed by the following
claims, which particularly point out and distinctly claim the subject
matter of the invention.